LMFDB - Embedded newform 289.10.a.h.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-7.00956 q^{2} +248.596 q^{3} -462.866 q^{4} -1624.49 q^{5} -1742.55 q^{6} -8782.15 q^{7} +6833.38 q^{8} +42117.0 q^{9} +O(q^{10})$	\(q-7.00956 q^{2} +248.596 q^{3} -462.866 q^{4} -1624.49 q^{5} -1742.55 q^{6} -8782.15 q^{7} +6833.38 q^{8} +42117.0 q^{9} +11386.9 q^{10} -52453.2 q^{11} -115067. q^{12} +14453.2 q^{13} +61559.0 q^{14} -403841. q^{15} +189088. q^{16} -295222. q^{18} -931720. q^{19} +751920. q^{20} -2.18321e6 q^{21} +367674. q^{22} +1.37040e6 q^{23} +1.69875e6 q^{24} +685836. q^{25} -101311. q^{26} +5.57701e6 q^{27} +4.06496e6 q^{28} -4.42440e6 q^{29} +2.83075e6 q^{30} -2.02178e6 q^{31} -4.82412e6 q^{32} -1.30397e7 q^{33} +1.42665e7 q^{35} -1.94945e7 q^{36} -1.55332e7 q^{37} +6.53095e6 q^{38} +3.59301e6 q^{39} -1.11007e7 q^{40} -8.35453e6 q^{41} +1.53033e7 q^{42} -2.42190e7 q^{43} +2.42788e7 q^{44} -6.84186e7 q^{45} -9.60592e6 q^{46} -2.77645e7 q^{47} +4.70066e7 q^{48} +3.67726e7 q^{49} -4.80741e6 q^{50} -6.68990e6 q^{52} +1.77712e6 q^{53} -3.90924e7 q^{54} +8.52096e7 q^{55} -6.00118e7 q^{56} -2.31622e8 q^{57} +3.10131e7 q^{58} -1.56378e8 q^{59} +1.86924e8 q^{60} +2.14150e8 q^{61} +1.41718e7 q^{62} -3.69878e8 q^{63} -6.29983e7 q^{64} -2.34791e7 q^{65} +9.14023e7 q^{66} +5.42382e7 q^{67} +3.40677e8 q^{69} -1.00002e8 q^{70} +2.38979e8 q^{71} +2.87802e8 q^{72} +3.24831e8 q^{73} +1.08881e8 q^{74} +1.70496e8 q^{75} +4.31262e8 q^{76} +4.60652e8 q^{77} -2.51854e7 q^{78} +3.05262e8 q^{79} -3.07172e8 q^{80} +5.57434e8 q^{81} +5.85616e7 q^{82} +1.35790e8 q^{83} +1.01053e9 q^{84} +1.69764e8 q^{86} -1.09989e9 q^{87} -3.58433e8 q^{88} +1.08876e9 q^{89} +4.79584e8 q^{90} -1.26930e8 q^{91} -6.34313e8 q^{92} -5.02607e8 q^{93} +1.94617e8 q^{94} +1.51357e9 q^{95} -1.19926e9 q^{96} +7.22732e8 q^{97} -2.57760e8 q^{98} -2.20917e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−7.00956	−0.309782	−0.154891	−	0.987932i	$-0.549503\pi$
$2$	−7.00956	−0.309782	−0.154891	+	0.987932i	$0.549503\pi$
$3$	248.596	1.77194	0.885969	−	0.463744i	$-0.153494\pi$
$3$	248.596	1.77194	0.885969	+	0.463744i	$0.153494\pi$
$4$	−462.866	−0.904035
$5$	−1624.49	−1.16239	−0.581194	−	0.813765i	$-0.697414\pi$
$5$	−1624.49	−1.16239	−0.581194	+	0.813765i	$0.697414\pi$
$6$	−1742.55	−0.548914
$7$	−8782.15	−1.38248	−0.691242	−	0.722624i	$-0.742936\pi$
$7$	−8782.15	−1.38248	−0.691242	+	0.722624i	$0.742936\pi$
$8$	6833.38	0.589835
$9$	42117.0	2.13977
$10$	11386.9	0.360087
$11$	−52453.2	−1.08020	−0.540101	−	0.841600i	$-0.681614\pi$
$11$	−52453.2	−1.08020	−0.540101	+	0.841600i	$0.681614\pi$
$12$	−115067.	−1.60190
$13$	14453.2	0.140352	0.0701761	−	0.997535i	$-0.477644\pi$
$13$	14453.2	0.140352	0.0701761	+	0.997535i	$0.477644\pi$
$14$	61559.0	0.428268
$15$	−403841.	−2.05968
$16$	189088.	0.721315
$17$	0	0
$17$	0	0
$18$	−295222.	−0.662861
$19$	−931720.	−1.64019	−0.820095	−	0.572227i	$-0.806080\pi$
$19$	−931720.	−1.64019	−0.820095	+	0.572227i	$0.806080\pi$
$20$	751920.	1.05084
$21$	−2.18321e6	−2.44968
$22$	367674.	0.334627
$23$	1.37040e6	1.02111	0.510556	−	0.859845i	$-0.329440\pi$
$23$	1.37040e6	1.02111	0.510556	+	0.859845i	$0.329440\pi$
$24$	1.69875e6	1.04515
$25$	685836.	0.351148
$26$	−101311.	−0.0434786
$27$	5.57701e6	2.01960
$28$	4.06496e6	1.24981
$29$	−4.42440e6	−1.16162	−0.580810	−	0.814039i	$-0.697264\pi$
$29$	−4.42440e6	−1.16162	−0.580810	+	0.814039i	$0.697264\pi$
$30$	2.83075e6	0.638052
$31$	−2.02178e6	−0.393194	−0.196597	−	0.980484i	$-0.562989\pi$
$31$	−2.02178e6	−0.393194	−0.196597	+	0.980484i	$0.562989\pi$
$32$	−4.82412e6	−0.813286
$33$	−1.30397e7	−1.91405
$34$	0	0
$35$	1.42665e7	1.60698
$36$	−1.94945e7	−1.93442
$37$	−1.55332e7	−1.36255	−0.681277	−	0.732026i	$-0.738575\pi$
$37$	−1.55332e7	−1.36255	−0.681277	+	0.732026i	$0.738575\pi$
$38$	6.53095e6	0.508101
$39$	3.59301e6	0.248696
$40$	−1.11007e7	−0.685618
$41$	−8.35453e6	−0.461737	−0.230869	−	0.972985i	$-0.574157\pi$
$41$	−8.35453e6	−0.461737	−0.230869	+	0.972985i	$0.574157\pi$
$42$	1.53033e7	0.758865
$43$	−2.42190e7	−1.08031	−0.540154	−	0.841566i	$-0.681634\pi$
$43$	−2.42190e7	−1.08031	−0.540154	+	0.841566i	$0.681634\pi$
$44$	2.42788e7	0.976541
$45$	−6.84186e7	−2.48724
$46$	−9.60592e6	−0.316322
$47$	−2.77645e7	−0.829945	−0.414973	−	0.909834i	$-0.636209\pi$
$47$	−2.77645e7	−0.829945	−0.414973	+	0.909834i	$0.636209\pi$
$48$	4.70066e7	1.27813
$49$	3.67726e7	0.911260
$50$	−4.80741e6	−0.108779
$51$	0	0
$52$	−6.68990e6	−0.126883
$53$	1.77712e6	0.0309369	0.0154684	−	0.999880i	$-0.495076\pi$
$53$	1.77712e6	0.0309369	0.0154684	+	0.999880i	$0.495076\pi$
$54$	−3.90924e7	−0.625634
$55$	8.52096e7	1.25561
$56$	−6.00118e7	−0.815437
$57$	−2.31622e8	−2.90632
$58$	3.10131e7	0.359848
$59$	−1.56378e8	−1.68012	−0.840062	−	0.542491i	$-0.817481\pi$
$59$	−1.56378e8	−1.68012	−0.840062	+	0.542491i	$0.817481\pi$
$60$	1.86924e8	1.86203
$61$	2.14150e8	1.98031	0.990157	−	0.139959i	$-0.0446971\pi$
$61$	2.14150e8	1.98031	0.990157	+	0.139959i	$0.0446971\pi$
$62$	1.41718e7	0.121804
$63$	−3.69878e8	−2.95819
$64$	−6.29983e7	−0.469374
$65$	−2.34791e7	−0.163144
$66$	9.14023e7	0.592938
$67$	5.42382e7	0.328828	0.164414	−	0.986391i	$-0.447427\pi$
$67$	5.42382e7	0.328828	0.164414	+	0.986391i	$0.447427\pi$
$68$	0	0
$69$	3.40677e8	1.80935
$70$	−1.00002e8	−0.497814
$71$	2.38979e8	1.11608	0.558042	−	0.829812i	$-0.311553\pi$
$71$	2.38979e8	1.11608	0.558042	+	0.829812i	$0.311553\pi$
$72$	2.87802e8	1.26211
$73$	3.24831e8	1.33876	0.669382	−	0.742918i	$-0.266559\pi$
$73$	3.24831e8	1.33876	0.669382	+	0.742918i	$0.266559\pi$
$74$	1.08881e8	0.422094
$75$	1.70496e8	0.622212
$76$	4.31262e8	1.48279
$77$	4.60652e8	1.49336
$78$	−2.51854e7	−0.0770414
$79$	3.05262e8	0.881760	0.440880	−	0.897566i	$-0.354666\pi$
$79$	3.05262e8	0.881760	0.440880	+	0.897566i	$0.354666\pi$
$80$	−3.07172e8	−0.838449
$81$	5.57434e8	1.43884
$82$	5.85616e7	0.143038
$83$	1.35790e8	0.314062	0.157031	−	0.987594i	$-0.449808\pi$
$83$	1.35790e8	0.314062	0.157031	+	0.987594i	$0.449808\pi$
$84$	1.01053e9	2.21459
$85$	0	0
$86$	1.69764e8	0.334660
$87$	−1.09989e9	−2.05832
$88$	−3.58433e8	−0.637141
$89$	1.08876e9	1.83941	0.919703	−	0.392616i	$-0.128430\pi$
$89$	1.08876e9	1.83941	0.919703	+	0.392616i	$0.128430\pi$
$90$	4.79584e8	0.770502
$91$	−1.26930e8	−0.194035
$92$	−6.34313e8	−0.923121
$93$	−5.02607e8	−0.696716
$94$	1.94617e8	0.257102
$95$	1.51357e9	1.90654
$96$	−1.19926e9	−1.44109
$97$	7.22732e8	0.828904	0.414452	−	0.910071i	$-0.363973\pi$
$97$	7.22732e8	0.828904	0.414452	+	0.910071i	$0.363973\pi$
$98$	−2.57760e8	−0.282292
$99$	−2.20917e9	−2.31138
$100$	−3.17450e8	−0.317450
$101$	−2.47246e8	−0.236420	−0.118210	−	0.992989i	$-0.537716\pi$
$101$	−2.47246e8	−0.236420	−0.118210	+	0.992989i	$0.537716\pi$
$102$	0	0
$103$	1.21679e9	1.06524	0.532621	−	0.846354i	$-0.321207\pi$
$103$	1.21679e9	1.06524	0.532621	+	0.846354i	$0.321207\pi$
$104$	9.87644e7	0.0827847
$105$	3.54660e9	2.84748
$106$	−1.24569e7	−0.00958368
$107$	−4.94831e8	−0.364947	−0.182474	−	0.983211i	$-0.558410\pi$
$107$	−4.94831e8	−0.364947	−0.182474	+	0.983211i	$0.558410\pi$
$108$	−2.58141e9	−1.82579
$109$	−8.73972e8	−0.593032	−0.296516	−	0.955028i	$-0.595825\pi$
$109$	−8.73972e8	−0.593032	−0.296516	+	0.955028i	$0.595825\pi$
$110$	−5.97282e8	−0.388966
$111$	−3.86150e9	−2.41436
$112$	−1.66060e9	−0.997206
$113$	1.44323e9	0.832691	0.416345	−	0.909207i	$-0.363311\pi$
$113$	1.44323e9	0.832691	0.416345	+	0.909207i	$0.363311\pi$
$114$	1.62357e9	0.900324
$115$	−2.22620e9	−1.18693
$116$	2.04791e9	1.05014
$117$	6.08727e8	0.300321
$118$	1.09614e9	0.520471
$119$	0	0
$120$	−2.75960e9	−1.21487
$121$	3.93390e8	0.166836
$122$	−1.50110e9	−0.613465
$123$	−2.07690e9	−0.818170
$124$	9.35815e8	0.355461
$125$	2.05870e9	0.754219
$126$	2.59268e9	0.916394
$127$	1.54660e9	0.527547	0.263774	−	0.964585i	$-0.415033\pi$
$127$	1.54660e9	0.527547	0.263774	+	0.964585i	$0.415033\pi$
$128$	2.91154e9	0.958689
$129$	−6.02074e9	−1.91424
$130$	1.64578e8	0.0505390
$131$	3.97813e8	0.118021	0.0590104	−	0.998257i	$-0.481205\pi$
$131$	3.97813e8	0.118021	0.0590104	+	0.998257i	$0.481205\pi$
$132$	6.03562e9	1.73037
$133$	8.18251e9	2.26754
$134$	−3.80186e8	−0.101865
$135$	−9.05979e9	−2.34756
$136$	0	0
$137$	1.76046e8	0.0426956	0.0213478	−	0.999772i	$-0.493204\pi$
$137$	1.76046e8	0.0426956	0.0213478	+	0.999772i	$0.493204\pi$
$138$	−2.38800e9	−0.560503
$139$	1.08750e9	0.247094	0.123547	−	0.992339i	$-0.460573\pi$
$139$	1.08750e9	0.247094	0.123547	+	0.992339i	$0.460573\pi$
$140$	−6.60348e9	−1.45277
$141$	−6.90215e9	−1.47061
$142$	−1.67514e9	−0.345743
$143$	−7.58117e8	−0.151609
$144$	7.96384e9	1.54345
$145$	7.18739e9	1.35025
$146$	−2.27692e9	−0.414725
$147$	9.14153e9	1.61470
$148$	7.18980e9	1.23180
$149$	−1.37802e9	−0.229044	−0.114522	−	0.993421i	$-0.536534\pi$
$149$	−1.37802e9	−0.229044	−0.114522	+	0.993421i	$0.536534\pi$
$150$	−1.19510e9	−0.192750
$151$	1.19046e9	0.186345	0.0931726	−	0.995650i	$-0.470299\pi$
$151$	1.19046e9	0.186345	0.0931726	+	0.995650i	$0.470299\pi$
$152$	−6.36680e9	−0.967442
$153$	0	0
$154$	−3.22897e9	−0.462616
$155$	3.28436e9	0.457044
$156$	−1.66308e9	−0.224830
$157$	−5.46787e9	−0.718240	−0.359120	−	0.933291i	$-0.616923\pi$
$157$	−5.46787e9	−0.718240	−0.359120	+	0.933291i	$0.616923\pi$
$158$	−2.13975e9	−0.273153
$159$	4.41786e8	0.0548183
$160$	7.83672e9	0.945354
$161$	−1.20351e10	−1.41167
$162$	−3.90737e9	−0.445725
$163$	−8.81919e8	−0.0978553	−0.0489276	−	0.998802i	$-0.515580\pi$
$163$	−8.81919e8	−0.0978553	−0.0489276	+	0.998802i	$0.515580\pi$
$164$	3.86703e9	0.417427
$165$	2.11828e10	2.22487
$166$	−9.51827e8	−0.0972908
$167$	−6.76444e8	−0.0672988	−0.0336494	−	0.999434i	$-0.510713\pi$
$167$	−6.76444e8	−0.0672988	−0.0336494	+	0.999434i	$0.510713\pi$
$168$	−1.49187e10	−1.44491
$169$	−1.03956e10	−0.980301
$170$	0	0
$171$	−3.92413e10	−3.50963
$172$	1.12101e10	0.976636
$173$	7.28714e9	0.618514	0.309257	−	0.950978i	$-0.399920\pi$
$173$	7.28714e9	0.618514	0.309257	+	0.950978i	$0.399920\pi$
$174$	7.70974e9	0.637629
$175$	−6.02311e9	−0.485456
$176$	−9.91829e9	−0.779166
$177$	−3.88749e10	−2.97708
$178$	−7.63173e9	−0.569814
$179$	−7.99107e8	−0.0581790	−0.0290895	−	0.999577i	$-0.509261\pi$
$179$	−7.99107e8	−0.0581790	−0.0290895	+	0.999577i	$0.509261\pi$
$180$	3.16687e10	2.24855
$181$	−1.62217e10	−1.12342	−0.561711	−	0.827333i	$-0.689857\pi$
$181$	−1.62217e10	−1.12342	−0.561711	+	0.827333i	$0.689857\pi$
$182$	8.89726e8	0.0601084
$183$	5.32369e10	3.50900
$184$	9.36449e9	0.602288
$185$	2.52335e10	1.58382
$186$	3.52306e9	0.215830
$187$	0	0
$188$	1.28512e10	0.750300
$189$	−4.89782e10	−2.79206
$190$	−1.06094e10	−0.590611
$191$	2.65734e10	1.44476	0.722382	−	0.691494i	$-0.243047\pi$
$191$	2.65734e10	1.44476	0.722382	+	0.691494i	$0.243047\pi$
$192$	−1.56611e10	−0.831702
$193$	8.35519e8	0.0433460	0.0216730	−	0.999765i	$-0.493101\pi$
$193$	8.35519e8	0.0433460	0.0216730	+	0.999765i	$0.493101\pi$
$194$	−5.06603e9	−0.256779
$195$	−5.83681e9	−0.289081
$196$	−1.70208e10	−0.823811
$197$	−2.26220e10	−1.07012	−0.535061	−	0.844813i	$-0.679712\pi$
$197$	−2.26220e10	−1.07012	−0.535061	+	0.844813i	$0.679712\pi$
$198$	1.54853e10	0.716023
$199$	−7.37113e9	−0.333192	−0.166596	−	0.986025i	$-0.553278\pi$
$199$	−7.37113e9	−0.333192	−0.166596	+	0.986025i	$0.553278\pi$
$200$	4.68658e9	0.207119
$201$	1.34834e10	0.582663
$202$	1.73309e9	0.0732386
$203$	3.88558e10	1.60592
$204$	0	0
$205$	1.35718e10	0.536718
$206$	−8.52916e9	−0.329992
$207$	5.77173e10	2.18494
$208$	2.73294e9	0.101238
$209$	4.88717e10	1.77174
$210$	−2.48601e10	−0.882096
$211$	4.36911e10	1.51748	0.758739	−	0.651395i	$-0.225816\pi$
$211$	4.36911e10	1.51748	0.758739	+	0.651395i	$0.225816\pi$
$212$	−8.22571e8	−0.0279680
$213$	5.94093e10	1.97763
$214$	3.46855e9	0.113054
$215$	3.93434e10	1.25574
$216$	3.81099e10	1.19123
$217$	1.77556e10	0.543584
$218$	6.12616e9	0.183711
$219$	8.07516e10	2.37221
$220$	−3.94406e10	−1.13512
$221$	0	0
$222$	2.70674e10	0.747925
$223$	−4.77247e10	−1.29232	−0.646162	−	0.763201i	$-0.723627\pi$
$223$	−4.77247e10	−1.29232	−0.646162	+	0.763201i	$0.723627\pi$
$224$	4.23661e10	1.12435
$225$	2.88854e10	0.751375
$226$	−1.01164e10	−0.257952
$227$	1.11533e10	0.278795	0.139398	−	0.990236i	$-0.455483\pi$
$227$	1.11533e10	0.278795	0.139398	+	0.990236i	$0.455483\pi$
$228$	1.07210e11	2.62741
$229$	−3.24445e9	−0.0779617	−0.0389809	−	0.999240i	$-0.512411\pi$
$229$	−3.24445e9	−0.0779617	−0.0389809	+	0.999240i	$0.512411\pi$
$230$	1.56047e10	0.367689
$231$	1.14516e11	2.64614
$232$	−3.02336e10	−0.685164
$233$	−3.64924e10	−0.811149	−0.405575	−	0.914062i	$-0.632929\pi$
$233$	−3.64924e10	−0.811149	−0.405575	+	0.914062i	$0.632929\pi$
$234$	−4.26691e9	−0.0930340
$235$	4.51031e10	0.964719
$236$	7.23820e10	1.51889
$237$	7.58869e10	1.56242
$238$	0	0
$239$	−8.38967e10	−1.66324	−0.831619	−	0.555347i	$-0.812586\pi$
$239$	−8.38967e10	−1.66324	−0.831619	+	0.555347i	$0.812586\pi$
$240$	−7.63617e10	−1.48568
$241$	3.00413e10	0.573644	0.286822	−	0.957984i	$-0.407401\pi$
$241$	3.00413e10	0.573644	0.286822	+	0.957984i	$0.407401\pi$
$242$	−2.75749e9	−0.0516827
$243$	2.88037e10	0.529931
$244$	−9.91229e10	−1.79027
$245$	−5.97367e10	−1.05924
$246$	1.45582e10	0.253454
$247$	−1.34664e10	−0.230204
$248$	−1.38156e10	−0.231920
$249$	3.37568e10	0.556499
$250$	−1.44306e10	−0.233643
$251$	−4.24314e10	−0.674770	−0.337385	−	0.941367i	$-0.609542\pi$
$251$	−4.24314e10	−0.674770	−0.337385	+	0.941367i	$0.609542\pi$
$252$	1.71204e11	2.67431
$253$	−7.18820e10	−1.10301
$254$	−1.08410e10	−0.163425
$255$	0	0
$256$	1.18465e10	0.172390
$257$	−6.81051e10	−0.973824	−0.486912	−	0.873451i	$-0.661877\pi$
$257$	−6.81051e10	−0.973824	−0.486912	+	0.873451i	$0.661877\pi$
$258$	4.22027e10	0.592996
$259$	1.36415e11	1.88371
$260$	1.08677e10	0.147488
$261$	−1.86343e11	−2.48559
$262$	−2.78850e9	−0.0365607
$263$	5.16210e10	0.665313	0.332656	−	0.943048i	$-0.392055\pi$
$263$	5.16210e10	0.665313	0.332656	+	0.943048i	$0.392055\pi$
$264$	−8.91050e10	−1.12898
$265$	−2.88692e9	−0.0359607
$266$	−5.73558e10	−0.702441
$267$	2.70662e11	3.25931
$268$	−2.51050e10	−0.297272
$269$	−9.39280e10	−1.09373	−0.546865	−	0.837221i	$-0.684179\pi$
$269$	−9.39280e10	−1.09373	−0.546865	+	0.837221i	$0.684179\pi$
$270$	6.35051e10	0.727230
$271$	5.18776e10	0.584276	0.292138	−	0.956376i	$-0.405633\pi$
$271$	5.18776e10	0.584276	0.292138	+	0.956376i	$0.405633\pi$
$272$	0	0
$273$	−3.15544e10	−0.343818
$274$	−1.23400e9	−0.0132263
$275$	−3.59743e10	−0.379311
$276$	−1.57688e11	−1.63571
$277$	−3.86848e9	−0.0394804	−0.0197402	−	0.999805i	$-0.506284\pi$
$277$	−3.86848e9	−0.0394804	−0.0197402	+	0.999805i	$0.506284\pi$
$278$	−7.62288e9	−0.0765451
$279$	−8.51515e10	−0.841343
$280$	9.74885e10	0.947855
$281$	−8.99774e10	−0.860904	−0.430452	−	0.902613i	$-0.641646\pi$
$281$	−8.99774e10	−0.860904	−0.430452	+	0.902613i	$0.641646\pi$
$282$	4.83810e10	0.455569
$283$	1.82003e11	1.68671	0.843353	−	0.537360i	$-0.180578\pi$
$283$	1.82003e11	1.68671	0.843353	+	0.537360i	$0.180578\pi$
$284$	−1.10615e11	−1.00898
$285$	3.76267e11	3.37827
$286$	5.31407e9	0.0469656
$287$	7.33708e10	0.638344
$288$	−2.03178e11	−1.74024
$289$	0	0
$290$	−5.03804e10	−0.418284
$291$	1.79668e11	1.46877
$292$	−1.50353e11	−1.21029
$293$	−2.62335e10	−0.207947	−0.103973	−	0.994580i	$-0.533156\pi$
$293$	−2.62335e10	−0.207947	−0.103973	+	0.994580i	$0.533156\pi$
$294$	−6.40781e10	−0.500203
$295$	2.54034e11	1.95296
$296$	−1.06144e11	−0.803682
$297$	−2.92532e11	−2.18157
$298$	9.65934e9	0.0709536
$299$	1.98067e10	0.143315
$300$	−7.89169e10	−0.562502
$301$	2.12695e11	1.49351
$302$	−8.34459e9	−0.0577263
$303$	−6.14645e10	−0.418922
$304$	−1.76177e11	−1.18309
$305$	−3.47884e11	−2.30190
$306$	0	0
$307$	−1.12502e11	−0.722830	−0.361415	−	0.932405i	$-0.617706\pi$
$307$	−1.12502e11	−0.722830	−0.361415	+	0.932405i	$0.617706\pi$
$308$	−2.13220e11	−1.35005
$309$	3.02489e11	1.88754
$310$	−2.30219e10	−0.141584
$311$	−1.05036e11	−0.636674	−0.318337	−	0.947978i	$-0.603124\pi$
$311$	−1.05036e11	−0.636674	−0.318337	+	0.947978i	$0.603124\pi$
$312$	2.45524e10	0.146689
$313$	2.38828e11	1.40648	0.703242	−	0.710950i	$-0.251735\pi$
$313$	2.38828e11	1.40648	0.703242	+	0.710950i	$0.251735\pi$
$314$	3.83274e10	0.222498
$315$	6.00863e11	3.43857
$316$	−1.41295e11	−0.797142
$317$	8.68678e10	0.483161	0.241581	−	0.970381i	$-0.422334\pi$
$317$	8.68678e10	0.483161	0.241581	+	0.970381i	$0.422334\pi$
$318$	−3.09673e9	−0.0169817
$319$	2.32074e11	1.25478
$320$	1.02340e11	0.545595
$321$	−1.23013e11	−0.646664
$322$	8.43607e10	0.437309
$323$	0	0
$324$	−2.58017e11	−1.30076
$325$	9.91253e9	0.0492844
$326$	6.18186e9	0.0303138
$327$	−2.17266e11	−1.05082
$328$	−5.70897e10	−0.272349
$329$	2.43832e11	1.14739
$330$	−1.48482e11	−0.689225
$331$	−2.31728e11	−1.06109	−0.530546	−	0.847656i	$-0.678013\pi$
$331$	−2.31728e11	−1.06109	−0.530546	+	0.847656i	$0.678013\pi$
$332$	−6.28525e10	−0.283923
$333$	−6.54213e11	−2.91555
$334$	4.74157e9	0.0208479
$335$	−8.81093e10	−0.382226
$336$	−4.12820e11	−1.76699
$337$	−1.29186e11	−0.545610	−0.272805	−	0.962069i	$-0.587951\pi$
$337$	−1.29186e11	−0.545610	−0.272805	+	0.962069i	$0.587951\pi$
$338$	7.28686e10	0.303679
$339$	3.58782e11	1.47548
$340$	0	0
$341$	1.06049e11	0.424729
$342$	2.75064e11	1.08722
$343$	3.14488e10	0.122682
$344$	−1.65497e11	−0.637204
$345$	−5.53426e11	−2.10316
$346$	−5.10796e10	−0.191604
$347$	−3.89281e11	−1.44139	−0.720693	−	0.693254i	$-0.756176\pi$
$347$	−3.89281e11	−1.44139	−0.720693	+	0.693254i	$0.756176\pi$
$348$	5.09102e11	1.86079
$349$	−1.79089e11	−0.646181	−0.323090	−	0.946368i	$-0.604722\pi$
$349$	−1.79089e11	−0.646181	−0.323090	+	0.946368i	$0.604722\pi$
$350$	4.22194e10	0.150385
$351$	8.06058e10	0.283455
$352$	2.53040e11	0.878513
$353$	1.53076e11	0.524711	0.262355	−	0.964971i	$-0.415501\pi$
$353$	1.53076e11	0.524711	0.262355	+	0.964971i	$0.415501\pi$
$354$	2.72496e11	0.922244
$355$	−3.88219e11	−1.29732
$356$	−5.03950e11	−1.66289
$357$	0	0
$358$	5.60139e9	0.0180228
$359$	4.54830e11	1.44519	0.722593	−	0.691274i	$-0.242950\pi$
$359$	4.54830e11	1.44519	0.722593	+	0.691274i	$0.242950\pi$
$360$	−4.67530e11	−1.46706
$361$	5.45415e11	1.69022
$362$	1.13707e11	0.348016
$363$	9.77953e10	0.295623
$364$	5.87518e10	0.175414
$365$	−5.27683e11	−1.55616
$366$	−3.73167e11	−1.08702
$367$	2.38622e11	0.686616	0.343308	−	0.939223i	$-0.388453\pi$
$367$	2.38622e11	0.686616	0.343308	+	0.939223i	$0.388453\pi$
$368$	2.59127e11	0.736543
$369$	−3.51868e11	−0.988010
$370$	−1.76876e11	−0.490638
$371$	−1.56070e10	−0.0427697
$372$	2.32640e11	0.629856
$373$	2.17508e11	0.581816	0.290908	−	0.956751i	$-0.406043\pi$
$373$	2.17508e11	0.581816	0.290908	+	0.956751i	$0.406043\pi$
$374$	0	0
$375$	5.11784e11	1.33643
$376$	−1.89725e11	−0.489531
$377$	−6.39469e10	−0.163036
$378$	3.43316e11	0.864929
$379$	1.13663e11	0.282972	0.141486	−	0.989940i	$-0.454812\pi$
$379$	1.13663e11	0.282972	0.141486	+	0.989940i	$0.454812\pi$
$380$	−7.00579e11	−1.72358
$381$	3.84479e11	0.934782
$382$	−1.86268e11	−0.447562
$383$	−3.84471e11	−0.912996	−0.456498	−	0.889724i	$-0.650896\pi$
$383$	−3.84471e11	−0.912996	−0.456498	+	0.889724i	$0.650896\pi$
$384$	7.23797e11	1.69874
$385$	−7.48324e11	−1.73587
$386$	−5.85662e9	−0.0134278
$387$	−1.02003e12	−2.31161
$388$	−3.34528e11	−0.749359
$389$	4.29907e11	0.951921	0.475961	−	0.879467i	$-0.342100\pi$
$389$	4.29907e11	0.951921	0.475961	+	0.879467i	$0.342100\pi$
$390$	4.09135e10	0.0895520
$391$	0	0
$392$	2.51281e11	0.537493
$393$	9.88948e10	0.209126
$394$	1.58571e11	0.331504
$395$	−4.95894e11	−1.02495
$396$	1.02255e12	2.08957
$397$	7.51343e10	0.151803	0.0759017	−	0.997115i	$-0.475816\pi$
$397$	7.51343e10	0.151803	0.0759017	+	0.997115i	$0.475816\pi$
$398$	5.16683e10	0.103217
$399$	2.03414e12	4.01793
$400$	1.29684e11	0.253288
$401$	−4.04002e11	−0.780251	−0.390125	−	0.920762i	$-0.627568\pi$
$401$	−4.04002e11	−0.780251	−0.390125	+	0.920762i	$0.627568\pi$
$402$	−9.45128e10	−0.180498
$403$	−2.92213e10	−0.0551857
$404$	1.14442e11	0.213732
$405$	−9.05545e11	−1.67249
$406$	−2.72362e11	−0.497484
$407$	8.14767e11	1.47183
$408$	0	0
$409$	9.13773e11	1.61467	0.807334	−	0.590094i	$-0.200909\pi$
$409$	9.13773e11	1.61467	0.807334	+	0.590094i	$0.200909\pi$
$410$	−9.51326e10	−0.166265
$411$	4.37643e10	0.0756541
$412$	−5.63211e11	−0.963016
$413$	1.37333e12	2.32274
$414$	−4.04573e11	−0.676855
$415$	−2.20589e11	−0.365063
$416$	−6.97240e10	−0.114146
$417$	2.70348e11	0.437835
$418$	−3.42569e11	−0.548852
$419$	−1.00256e12	−1.58909	−0.794546	−	0.607204i	$-0.792291\pi$
$419$	−1.00256e12	−1.58909	−0.794546	+	0.607204i	$0.792291\pi$
$420$	−1.64160e12	−2.57422
$421$	−2.42505e11	−0.376229	−0.188114	−	0.982147i	$-0.560238\pi$
$421$	−2.42505e11	−0.376229	−0.188114	+	0.982147i	$0.560238\pi$
$422$	−3.06256e11	−0.470087
$423$	−1.16936e12	−1.77589
$424$	1.21438e10	0.0182477
$425$	0	0
$426$	−4.16433e11	−0.612635
$427$	−1.88070e12	−2.73775
$428$	2.29040e11	0.329925
$429$	−1.88465e11	−0.268641
$430$	−2.75780e11	−0.389004
$431$	9.69783e11	1.35371	0.676857	−	0.736114i	$-0.263341\pi$
$431$	9.69783e11	1.35371	0.676857	+	0.736114i	$0.263341\pi$
$432$	1.05455e12	1.45677
$433$	−1.45177e12	−1.98473	−0.992366	−	0.123330i	$-0.960642\pi$
$433$	−1.45177e12	−1.98473	−0.992366	+	0.123330i	$0.960642\pi$
$434$	−1.24459e11	−0.168392
$435$	1.78676e12	2.39257
$436$	4.04532e11	0.536122
$437$	−1.27683e12	−1.67482
$438$	−5.66033e11	−0.734867
$439$	4.81662e11	0.618945	0.309473	−	0.950908i	$-0.399847\pi$
$439$	4.81662e11	0.618945	0.309473	+	0.950908i	$0.399847\pi$
$440$	5.82270e11	0.740606
$441$	1.54875e12	1.94988
$442$	0	0
$443$	7.63906e11	0.942374	0.471187	−	0.882033i	$-0.343826\pi$
$443$	7.63906e11	0.942374	0.471187	+	0.882033i	$0.343826\pi$
$444$	1.78736e12	2.18267
$445$	−1.76868e12	−2.13810
$446$	3.34529e11	0.400338
$447$	−3.42571e11	−0.405852
$448$	5.53261e11	0.648902
$449$	6.18932e11	0.718678	0.359339	−	0.933207i	$-0.383002\pi$
$449$	6.18932e11	0.718678	0.359339	+	0.933207i	$0.383002\pi$
$450$	−2.02474e11	−0.232762
$451$	4.38222e11	0.498769
$452$	−6.68024e11	−0.752782
$453$	2.95943e11	0.330192
$454$	−7.81795e10	−0.0863657
$455$	2.06197e11	0.225544
$456$	−1.58276e12	−1.71425
$457$	7.94938e11	0.852532	0.426266	−	0.904598i	$-0.359829\pi$
$457$	7.94938e11	0.852532	0.426266	+	0.904598i	$0.359829\pi$
$458$	2.27422e10	0.0241511
$459$	0	0
$460$	1.03043e12	1.07303
$461$	1.01020e12	1.04173	0.520863	−	0.853640i	$-0.325610\pi$
$461$	1.01020e12	1.04173	0.520863	+	0.853640i	$0.325610\pi$
$462$	−8.02709e11	−0.819727
$463$	1.72927e12	1.74883	0.874414	−	0.485180i	$-0.161246\pi$
$463$	1.72927e12	1.74883	0.874414	+	0.485180i	$0.161246\pi$
$464$	−8.36604e11	−0.837893
$465$	8.16479e11	0.809854
$466$	2.55796e11	0.251279
$467$	−6.73051e10	−0.0654820	−0.0327410	−	0.999464i	$-0.510424\pi$
$467$	−6.73051e10	−0.0654820	−0.0327410	+	0.999464i	$0.510424\pi$
$468$	−2.81759e11	−0.271501
$469$	−4.76328e11	−0.454599
$470$	−3.16153e11	−0.298852
$471$	−1.35929e12	−1.27268
$472$	−1.06859e12	−0.990996
$473$	1.27036e12	1.16695
$474$	−5.31934e11	−0.484011
$475$	−6.39007e11	−0.575949
$476$	0	0
$477$	7.48472e10	0.0661977
$478$	5.88079e11	0.515241
$479$	2.10574e12	1.82766	0.913830	−	0.406097i	$-0.133111\pi$
$479$	2.10574e12	1.82766	0.913830	+	0.406097i	$0.133111\pi$
$480$	1.94818e12	1.67511
$481$	−2.24505e11	−0.191238
$482$	−2.10577e11	−0.177704
$483$	−2.99188e12	−2.50139
$484$	−1.82087e11	−0.150826
$485$	−1.17407e12	−0.963509
$486$	−2.01901e11	−0.164163
$487$	1.06942e12	0.861522	0.430761	−	0.902466i	$-0.358245\pi$
$487$	1.06942e12	0.861522	0.430761	+	0.902466i	$0.358245\pi$
$488$	1.46337e12	1.16806
$489$	−2.19242e11	−0.173394
$490$	4.18728e11	0.328133
$491$	3.63691e10	0.0282400	0.0141200	−	0.999900i	$-0.495505\pi$
$491$	3.63691e10	0.0282400	0.0141200	+	0.999900i	$0.495505\pi$
$492$	9.61329e11	0.739654
$493$	0	0
$494$	9.43932e10	0.0713131
$495$	3.58877e12	2.68672
$496$	−3.82296e11	−0.283617
$497$	−2.09875e12	−1.54297
$498$	−2.36621e11	−0.172393
$499$	1.51766e12	1.09578	0.547888	−	0.836552i	$-0.315432\pi$
$499$	1.51766e12	1.09578	0.547888	+	0.836552i	$0.315432\pi$
$500$	−9.52901e11	−0.681840
$501$	−1.68161e11	−0.119249
$502$	2.97426e11	0.209031
$503$	−1.28396e12	−0.894328	−0.447164	−	0.894452i	$-0.647566\pi$
$503$	−1.28396e12	−0.894328	−0.447164	+	0.894452i	$0.647566\pi$
$504$	−2.52752e12	−1.74485
$505$	4.01649e11	0.274812
$506$	5.03861e11	0.341691
$507$	−2.58431e12	−1.73703
$508$	−7.15869e11	−0.476921
$509$	−1.62951e12	−1.07604	−0.538018	−	0.842934i	$-0.680827\pi$
$509$	−1.62951e12	−1.07604	−0.538018	+	0.842934i	$0.680827\pi$
$510$	0	0
$511$	−2.85271e12	−1.85082
$512$	−1.57375e12	−1.01209
$513$	−5.19622e12	−3.31252
$514$	4.77387e11	0.301673
$515$	−1.97666e12	−1.23822
$516$	2.78680e12	1.73054
$517$	1.45634e12	0.896509
$518$	−9.56210e11	−0.583538
$519$	1.81155e12	1.09597
$520$	−1.60442e11	−0.0962280
$521$	−2.49853e12	−1.48565	−0.742823	−	0.669488i	$-0.766513\pi$
$521$	−2.49853e12	−1.48565	−0.742823	+	0.669488i	$0.766513\pi$
$522$	1.30618e12	0.769992
$523$	−2.86852e12	−1.67649	−0.838244	−	0.545295i	$-0.816417\pi$
$523$	−2.86852e12	−1.67649	−0.838244	+	0.545295i	$0.816417\pi$
$524$	−1.84134e11	−0.106695
$525$	−1.49732e12	−0.860198
$526$	−3.61841e11	−0.206102
$527$	0	0
$528$	−2.46565e12	−1.38063
$529$	7.68525e10	0.0426685
$530$	2.02360e10	0.0111400
$531$	−6.58617e12	−3.59507
$532$	−3.78741e12	−2.04993
$533$	−1.20750e11	−0.0648059
$534$	−1.89722e12	−1.00968
$535$	8.03847e11	0.424210
$536$	3.70630e11	0.193954
$537$	−1.98655e11	−0.103090
$538$	6.58394e11	0.338817
$539$	−1.92884e12	−0.984344
$540$	4.19347e12	2.12227
$541$	5.94020e11	0.298135	0.149068	−	0.988827i	$-0.452373\pi$
$541$	5.94020e11	0.298135	0.149068	+	0.988827i	$0.452373\pi$
$542$	−3.63639e11	−0.180998
$543$	−4.03266e12	−1.99064
$544$	0	0
$545$	1.41976e12	0.689334
$546$	2.21182e11	0.106508
$547$	6.01511e11	0.287277	0.143639	−	0.989630i	$-0.454120\pi$
$547$	6.01511e11	0.287277	0.143639	+	0.989630i	$0.454120\pi$
$548$	−8.14857e10	−0.0385984
$549$	9.01937e12	4.23741
$550$	2.52164e11	0.117503
$551$	4.12231e12	1.90528
$552$	2.32798e12	1.06722
$553$	−2.68085e12	−1.21902
$554$	2.71163e10	0.0122303
$555$	6.27296e12	2.80643
$556$	−5.03366e11	−0.223382
$557$	2.06033e12	0.906959	0.453480	−	0.891267i	$-0.350182\pi$
$557$	2.06033e12	0.906959	0.453480	+	0.891267i	$0.350182\pi$
$558$	5.96874e11	0.260633
$559$	−3.50042e11	−0.151624
$560$	2.69763e12	1.15914
$561$	0	0
$562$	6.30702e11	0.266692
$563$	2.45629e12	1.03037	0.515183	−	0.857080i	$-0.327724\pi$
$563$	2.45629e12	1.03037	0.515183	+	0.857080i	$0.327724\pi$
$564$	3.19477e12	1.32949
$565$	−2.34452e12	−0.967910
$566$	−1.27576e12	−0.522511
$567$	−4.89547e12	−1.98917
$568$	1.63304e12	0.658306
$569$	−3.63389e11	−0.145334	−0.0726669	−	0.997356i	$-0.523151\pi$
$569$	−3.63389e11	−0.145334	−0.0726669	+	0.997356i	$0.523151\pi$
$570$	−2.63747e12	−1.04653
$571$	2.95458e11	0.116314	0.0581572	−	0.998307i	$-0.481478\pi$
$571$	2.95458e11	0.116314	0.0581572	+	0.998307i	$0.481478\pi$
$572$	3.50907e11	0.137060
$573$	6.60605e12	2.56003
$574$	−5.14297e11	−0.197747
$575$	9.39871e11	0.358561
$576$	−2.65330e12	−1.00435
$577$	−3.92296e12	−1.47341	−0.736703	−	0.676217i	$-0.763618\pi$
$577$	−3.92296e12	−1.47341	−0.736703	+	0.676217i	$0.763618\pi$
$578$	0	0
$579$	2.07707e11	0.0768064
$580$	−3.32680e12	−1.22068
$581$	−1.19253e12	−0.434186
$582$	−1.25940e12	−0.454997
$583$	−9.32159e10	−0.0334181
$584$	2.21969e12	0.789650
$585$	−9.88869e11	−0.349090
$586$	1.83885e11	0.0644181
$587$	−9.38917e11	−0.326404	−0.163202	−	0.986593i	$-0.552182\pi$
$587$	−9.38917e11	−0.326404	−0.163202	+	0.986593i	$0.552182\pi$
$588$	−4.23130e12	−1.45974
$589$	1.88374e12	0.644913
$590$	−1.78067e12	−0.604990
$591$	−5.62375e12	−1.89619
$592$	−2.93715e12	−0.982831
$593$	−1.11640e12	−0.370743	−0.185372	−	0.982668i	$-0.559349\pi$
$593$	−1.11640e12	−0.370743	−0.185372	+	0.982668i	$0.559349\pi$
$594$	2.05052e12	0.675811
$595$	0	0
$596$	6.37841e11	0.207064
$597$	−1.83243e12	−0.590396
$598$	−1.38837e11	−0.0443965
$599$	3.47623e12	1.10329	0.551643	−	0.834080i	$-0.314001\pi$
$599$	3.47623e12	1.10329	0.551643	+	0.834080i	$0.314001\pi$
$600$	1.16506e12	0.367003
$601$	−2.69936e12	−0.843969	−0.421984	−	0.906603i	$-0.638666\pi$
$601$	−2.69936e12	−0.843969	−0.421984	+	0.906603i	$0.638666\pi$
$602$	−1.49090e12	−0.462661
$603$	2.28435e12	0.703615
$604$	−5.51023e11	−0.168463
$605$	−6.39058e11	−0.193928
$606$	4.30839e11	0.129774
$607$	2.93363e10	0.00877114	0.00438557	−	0.999990i	$-0.498604\pi$
$607$	2.93363e10	0.00877114	0.00438557	+	0.999990i	$0.498604\pi$
$608$	4.49473e12	1.33394
$609$	9.65940e12	2.84559
$610$	2.43852e12	0.713085
$611$	−4.01286e11	−0.116485
$612$	0	0
$613$	8.08148e11	0.231163	0.115582	−	0.993298i	$-0.463127\pi$
$613$	8.08148e11	0.231163	0.115582	+	0.993298i	$0.463127\pi$
$614$	7.88587e11	0.223919
$615$	3.37391e12	0.951032
$616$	3.14781e12	0.880837
$617$	−6.66373e12	−1.85112	−0.925559	−	0.378603i	$-0.876405\pi$
$617$	−6.66373e12	−1.85112	−0.925559	+	0.378603i	$0.876405\pi$
$618$	−2.12032e12	−0.584726
$619$	−3.87308e12	−1.06035	−0.530175	−	0.847888i	$-0.677874\pi$
$619$	−3.87308e12	−1.06035	−0.530175	+	0.847888i	$0.677874\pi$
$620$	−1.52022e12	−0.413184
$621$	7.64276e12	2.06223
$622$	7.36257e11	0.197230
$623$	−9.56166e12	−2.54295
$624$	6.79397e11	0.179388
$625$	−4.68385e12	−1.22784
$626$	−1.67408e12	−0.435703
$627$	1.21493e13	3.13941
$628$	2.53089e12	0.649315
$629$	0	0
$630$	−4.21178e12	−1.06521
$631$	−5.76051e12	−1.44653	−0.723267	−	0.690568i	$-0.757360\pi$
$631$	−5.76051e12	−1.44653	−0.723267	+	0.690568i	$0.757360\pi$
$632$	2.08597e12	0.520093
$633$	1.08614e13	2.68888
$634$	−6.08905e11	−0.149674
$635$	−2.51243e12	−0.613215
$636$	−2.04488e11	−0.0495576
$637$	5.31483e11	0.127897
$638$	−1.62674e12	−0.388709
$639$	1.00651e13	2.38816
$640$	−4.72976e12	−1.11437
$641$	2.94103e12	0.688079	0.344039	−	0.938955i	$-0.388205\pi$
$641$	2.94103e12	0.688079	0.344039	+	0.938955i	$0.388205\pi$
$642$	8.62267e11	0.200325
$643$	4.08339e12	0.942044	0.471022	−	0.882122i	$-0.343885\pi$
$643$	4.08339e12	0.942044	0.471022	+	0.882122i	$0.343885\pi$
$644$	5.57064e12	1.27620
$645$	9.78062e12	2.22509
$646$	0	0
$647$	4.11077e12	0.922262	0.461131	−	0.887332i	$-0.347444\pi$
$647$	4.11077e12	0.922262	0.461131	+	0.887332i	$0.347444\pi$
$648$	3.80916e12	0.848676
$649$	8.20252e12	1.81487
$650$	−6.94825e10	−0.0152674
$651$	4.41397e12	0.963198
$652$	4.08210e11	0.0884646
$653$	4.38279e12	0.943282	0.471641	−	0.881791i	$-0.343662\pi$
$653$	4.38279e12	0.943282	0.471641	+	0.881791i	$0.343662\pi$
$654$	1.52294e12	0.325524
$655$	−6.46243e11	−0.137186
$656$	−1.57975e12	−0.333058
$657$	1.36809e13	2.86464
$658$	−1.70916e12	−0.355439
$659$	1.21956e12	0.251894	0.125947	−	0.992037i	$-0.459803\pi$
$659$	1.21956e12	0.251894	0.125947	+	0.992037i	$0.459803\pi$
$660$	−9.80479e12	−2.01136
$661$	−6.37742e12	−1.29939	−0.649694	−	0.760196i	$-0.725103\pi$
$661$	−6.37742e12	−1.29939	−0.649694	+	0.760196i	$0.725103\pi$
$662$	1.62431e12	0.328707
$663$	0	0
$664$	9.27904e11	0.185245
$665$	−1.32924e13	−2.63576
$666$	4.58574e12	0.903183
$667$	−6.06322e12	−1.18614
$668$	3.13103e11	0.0608405
$669$	−1.18642e13	−2.28992
$670$	6.17608e11	0.118407
$671$	−1.12329e13	−2.13914
$672$	1.05321e13	1.99229
$673$	1.25663e12	0.236124	0.118062	−	0.993006i	$-0.462332\pi$
$673$	1.25663e12	0.236124	0.118062	+	0.993006i	$0.462332\pi$
$674$	9.05539e11	0.169020
$675$	3.82491e12	0.709177
$676$	4.81177e12	0.886227
$677$	−9.83587e11	−0.179955	−0.0899775	−	0.995944i	$-0.528679\pi$
$677$	−9.83587e11	−0.179955	−0.0899775	+	0.995944i	$0.528679\pi$
$678$	−2.51491e12	−0.457076
$679$	−6.34714e12	−1.14595
$680$	0	0
$681$	2.77266e12	0.494008
$682$	−7.43357e11	−0.131573
$683$	5.43786e12	0.956169	0.478084	−	0.878314i	$-0.341331\pi$
$683$	5.43786e12	0.956169	0.478084	+	0.878314i	$0.341331\pi$
$684$	1.81635e13	3.17283
$685$	−2.85985e11	−0.0496289
$686$	−2.20443e11	−0.0380047
$687$	−8.06558e11	−0.138143
$688$	−4.57952e12	−0.779242
$689$	2.56852e10	0.00434206
$690$	3.87927e12	0.651522
$691$	−7.35157e12	−1.22667	−0.613337	−	0.789821i	$-0.710173\pi$
$691$	−7.35157e12	−1.22667	−0.613337	+	0.789821i	$0.710173\pi$
$692$	−3.37297e12	−0.559159
$693$	1.94013e13	3.19544
$694$	2.72869e12	0.446515
$695$	−1.76663e12	−0.287219
$696$	−7.51597e12	−1.21407
$697$	0	0
$698$	1.25533e12	0.200175
$699$	−9.07187e12	−1.43731
$700$	2.78790e12	0.438869
$701$	−2.91902e12	−0.456568	−0.228284	−	0.973595i	$-0.573311\pi$
$701$	−2.91902e12	−0.456568	−0.228284	+	0.973595i	$0.573311\pi$
$702$	−5.65011e11	−0.0878092
$703$	1.44726e13	2.23485
$704$	3.30446e12	0.507019
$705$	1.12125e13	1.70942
$706$	−1.07299e12	−0.162546
$707$	2.17136e12	0.326846
$708$	1.79939e13	2.69138
$709$	−1.06024e13	−1.57577	−0.787887	−	0.615819i	$-0.788825\pi$
$709$	−1.06024e13	−1.57577	−0.787887	+	0.615819i	$0.788825\pi$
$710$	2.72124e12	0.401887
$711$	1.28567e13	1.88676
$712$	7.43992e12	1.08495
$713$	−2.77066e12	−0.401495
$714$	0	0
$715$	1.23155e12	0.176228
$716$	3.69880e11	0.0525959
$717$	−2.08564e13	−2.94716
$718$	−3.18816e12	−0.447692
$719$	1.29087e13	1.80137	0.900683	−	0.434477i	$-0.143067\pi$
$719$	1.29087e13	1.80137	0.900683	+	0.434477i	$0.143067\pi$
$720$	−1.29372e13	−1.79408
$721$	−1.06860e13	−1.47268
$722$	−3.82312e12	−0.523601
$723$	7.46816e12	1.01646
$724$	7.50848e12	1.01561
$725$	−3.03441e12	−0.407900
$726$	−6.85502e11	−0.0915786
$727$	9.77625e12	1.29798	0.648989	−	0.760797i	$-0.275192\pi$
$727$	9.77625e12	1.29798	0.648989	+	0.760797i	$0.275192\pi$
$728$	−8.67364e11	−0.114448
$729$	−3.81150e12	−0.499830
$730$	3.69883e12	0.482071
$731$	0	0
$732$	−2.46416e13	−3.17226
$733$	4.87882e11	0.0624233	0.0312116	−	0.999513i	$-0.490063\pi$
$733$	4.87882e11	0.0624233	0.0312116	+	0.999513i	$0.490063\pi$
$734$	−1.67264e12	−0.212701
$735$	−1.48503e13	−1.87690
$736$	−6.61099e12	−0.830455
$737$	−2.84497e12	−0.355201
$738$	2.46644e12	0.306067
$739$	−1.08646e13	−1.34003	−0.670017	−	0.742346i	$-0.733713\pi$
$739$	−1.08646e13	−1.34003	−0.670017	+	0.742346i	$0.733713\pi$
$740$	−1.16797e13	−1.43183
$741$	−3.34768e12	−0.407908
$742$	1.09398e11	0.0132493
$743$	1.10195e13	1.32651	0.663257	−	0.748392i	$-0.269174\pi$
$743$	1.10195e13	1.32651	0.663257	+	0.748392i	$0.269174\pi$
$744$	−3.43451e12	−0.410947
$745$	2.23858e12	0.266238
$746$	−1.52464e12	−0.180236
$747$	5.71907e12	0.672020
$748$	0	0
$749$	4.34568e12	0.504533
$750$	−3.58738e12	−0.414001
$751$	3.58977e12	0.411801	0.205900	−	0.978573i	$-0.433988\pi$
$751$	3.58977e12	0.411801	0.205900	+	0.978573i	$0.433988\pi$
$752$	−5.24995e12	−0.598652
$753$	−1.05483e13	−1.19565
$754$	4.48239e11	0.0505055
$755$	−1.93389e12	−0.216606
$756$	2.26703e13	2.52412
$757$	−2.28696e12	−0.253120	−0.126560	−	0.991959i	$-0.540394\pi$
$757$	−2.28696e12	−0.253120	−0.126560	+	0.991959i	$0.540394\pi$
$758$	−7.96729e11	−0.0876596
$759$	−1.78696e13	−1.95446
$760$	1.03428e13	1.12454
$761$	−1.64862e13	−1.78193	−0.890963	−	0.454075i	$-0.849970\pi$
$761$	−1.64862e13	−1.78193	−0.890963	+	0.454075i	$0.849970\pi$
$762$	−2.69503e12	−0.289578
$763$	7.67536e12	0.819857
$764$	−1.22999e13	−1.30612
$765$	0	0
$766$	2.69497e12	0.282829
$767$	−2.26016e12	−0.235809
$768$	2.94500e12	0.305464
$769$	1.24332e13	1.28208	0.641041	−	0.767507i	$-0.278503\pi$
$769$	1.24332e13	1.28208	0.641041	+	0.767507i	$0.278503\pi$
$770$	5.24542e12	0.537740
$771$	−1.69307e13	−1.72556
$772$	−3.86734e11	−0.0391863
$773$	1.06939e12	0.107728	0.0538642	−	0.998548i	$-0.482846\pi$
$773$	1.06939e12	0.107728	0.0538642	+	0.998548i	$0.482846\pi$
$774$	7.14997e12	0.716093
$775$	−1.38661e12	−0.138069
$776$	4.93870e12	0.488917
$777$	3.39123e13	3.33781
$778$	−3.01346e12	−0.294888
$779$	7.78409e12	0.757337
$780$	2.70166e12	0.261339
$781$	−1.25352e13	−1.20560
$782$	0	0
$783$	−2.46750e13	−2.34600
$784$	6.95328e12	0.657305
$785$	8.88249e12	0.834875
$786$	−6.93209e11	−0.0647833
$787$	−1.51542e13	−1.40815	−0.704073	−	0.710128i	$-0.748637\pi$
$787$	−1.51542e13	−1.40815	−0.704073	+	0.710128i	$0.748637\pi$
$788$	1.04710e13	0.967429
$789$	1.28328e13	1.17889
$790$	3.47600e12	0.317510
$791$	−1.26747e13	−1.15118
$792$	−1.50961e13	−1.36333
$793$	3.09516e12	0.277942
$794$	−5.26659e11	−0.0470259
$795$	−7.17677e11	−0.0637201
$796$	3.41184e12	0.301218
$797$	1.45731e12	0.127935	0.0639675	−	0.997952i	$-0.479625\pi$
$797$	1.45731e12	0.127935	0.0639675	+	0.997952i	$0.479625\pi$
$798$	−1.42584e13	−1.24468
$799$	0	0
$800$	−3.30855e12	−0.285583
$801$	4.58554e13	3.93590
$802$	2.83188e12	0.241707
$803$	−1.70384e13	−1.44614
$804$	−6.24101e12	−0.526748
$805$	1.95509e13	1.64091
$806$	2.04828e11	0.0170955
$807$	−2.33501e13	−1.93802
$808$	−1.68953e12	−0.139449
$809$	3.25669e12	0.267306	0.133653	−	0.991028i	$-0.457329\pi$
$809$	3.25669e12	0.267306	0.133653	+	0.991028i	$0.457329\pi$
$810$	6.34747e12	0.518106
$811$	−3.09214e12	−0.250995	−0.125498	−	0.992094i	$-0.540053\pi$
$811$	−3.09214e12	−0.250995	−0.125498	+	0.992094i	$0.540053\pi$
$812$	−1.79850e13	−1.45181
$813$	1.28966e13	1.03530
$814$	−5.71116e12	−0.455947
$815$	1.43267e12	0.113746
$816$	0	0
$817$	2.25653e13	1.77191
$818$	−6.40515e12	−0.500195
$819$	−5.34593e12	−0.415189
$820$	−6.28194e12	−0.485212
$821$	−2.16404e13	−1.66235	−0.831173	−	0.556014i	$-0.812330\pi$
$821$	−2.16404e13	−1.66235	−0.831173	+	0.556014i	$0.812330\pi$
$822$	−3.06769e11	−0.0234362
$823$	−1.30860e13	−0.994274	−0.497137	−	0.867672i	$-0.665615\pi$
$823$	−1.30860e13	−0.994274	−0.497137	+	0.867672i	$0.665615\pi$
$824$	8.31479e12	0.628317
$825$	−8.94306e12	−0.672115
$826$	−9.62647e12	−0.719543
$827$	2.09145e13	1.55479	0.777395	−	0.629012i	$-0.216541\pi$
$827$	2.09145e13	1.55479	0.777395	+	0.629012i	$0.216541\pi$
$828$	−2.67154e13	−1.97526
$829$	1.62798e13	1.19716	0.598582	−	0.801062i	$-0.295731\pi$
$829$	1.62798e13	1.19716	0.598582	+	0.801062i	$0.295731\pi$
$830$	1.54623e12	0.113090
$831$	−9.61688e11	−0.0699568
$832$	−9.10529e11	−0.0658777
$833$	0	0
$834$	−1.89502e12	−0.135633
$835$	1.09887e12	0.0782274
$836$	−2.26211e13	−1.60171
$837$	−1.12755e13	−0.794093
$838$	7.02753e12	0.492271
$839$	1.90100e13	1.32450	0.662250	−	0.749283i	$-0.269601\pi$
$839$	1.90100e13	1.32450	0.662250	+	0.749283i	$0.269601\pi$
$840$	2.42353e13	1.67954
$841$	5.06820e12	0.349359
$842$	1.69986e12	0.116549
$843$	−2.23680e13	−1.52547
$844$	−2.02231e13	−1.37185
$845$	1.68875e13	1.13949
$846$	8.19669e12	0.550138
$847$	−3.45481e12	−0.230648
$848$	3.36034e11	0.0223152
$849$	4.52452e13	2.98874
$850$	0	0
$851$	−2.12868e13	−1.39132
$852$	−2.74985e13	−1.78785
$853$	2.05191e13	1.32705	0.663526	−	0.748153i	$-0.269059\pi$
$853$	2.05191e13	1.32705	0.663526	+	0.748153i	$0.269059\pi$
$854$	1.31829e13	0.848105
$855$	6.37470e13	4.07955
$856$	−3.38137e12	−0.215259
$857$	−2.96637e12	−0.187850	−0.0939250	−	0.995579i	$-0.529941\pi$
$857$	−2.96637e12	−0.187850	−0.0939250	+	0.995579i	$0.529941\pi$
$858$	1.32106e12	0.0832202
$859$	1.06159e13	0.665257	0.332628	−	0.943058i	$-0.392065\pi$
$859$	1.06159e13	0.665257	0.332628	+	0.943058i	$0.392065\pi$
$860$	−1.82107e13	−1.13523
$861$	1.82397e13	1.13111
$862$	−6.79775e12	−0.419356
$863$	−1.32698e13	−0.814356	−0.407178	−	0.913349i	$-0.633487\pi$
$863$	−1.32698e13	−0.814356	−0.407178	+	0.913349i	$0.633487\pi$
$864$	−2.69042e13	−1.64251
$865$	−1.18379e13	−0.718954
$866$	1.01763e13	0.614833
$867$	0	0
$868$	−8.21847e12	−0.491419
$869$	−1.60120e13	−0.952479
$870$	−1.25244e13	−0.741173
$871$	7.83917e11	0.0461518
$872$	−5.97218e12	−0.349791
$873$	3.04393e13	1.77366
$874$	8.95003e12	0.518828
$875$	−1.80798e13	−1.04269
$876$	−3.73772e13	−2.14456
$877$	1.84228e13	1.05162	0.525808	−	0.850603i	$-0.323763\pi$
$877$	1.84228e13	1.05162	0.525808	+	0.850603i	$0.323763\pi$
$878$	−3.37624e12	−0.191738
$879$	−6.52155e12	−0.368469
$880$	1.61121e13	0.905694
$881$	−1.68763e12	−0.0943813	−0.0471907	−	0.998886i	$-0.515027\pi$
$881$	−1.68763e12	−0.0943813	−0.0471907	+	0.998886i	$0.515027\pi$
$882$	−1.08561e13	−0.604038
$883$	4.77050e12	0.264083	0.132042	−	0.991244i	$-0.457847\pi$
$883$	4.77050e12	0.264083	0.132042	+	0.991244i	$0.457847\pi$
$884$	0	0
$885$	6.31518e13	3.46052
$886$	−5.35464e12	−0.291930
$887$	1.25350e13	0.679936	0.339968	−	0.940437i	$-0.389584\pi$
$887$	1.25350e13	0.679936	0.339968	+	0.940437i	$0.389584\pi$
$888$	−2.63871e13	−1.42408
$889$	−1.35825e13	−0.729325
$890$	1.23977e13	0.662346
$891$	−2.92392e13	−1.55423
$892$	2.20901e13	1.16831
$893$	2.58687e13	1.36127
$894$	2.40128e12	0.125725
$895$	1.29814e12	0.0676266
$896$	−2.55696e13	−1.32537
$897$	4.92388e12	0.253946
$898$	−4.33844e12	−0.222633
$899$	8.94518e12	0.456742
$900$	−1.33701e13	−0.679269
$901$	0	0
$902$	−3.07174e12	−0.154510
$903$	5.28751e13	2.64640
$904$	9.86217e12	0.491150
$905$	2.63520e13	1.30585
$906$	−2.07443e12	−0.102288
$907$	−1.39545e13	−0.684668	−0.342334	−	0.939578i	$-0.611217\pi$
$907$	−1.39545e13	−0.684668	−0.342334	+	0.939578i	$0.611217\pi$
$908$	−5.16247e12	−0.252041
$909$	−1.04133e13	−0.505883
$910$	−1.44535e12	−0.0698693
$911$	1.75468e13	0.844045	0.422022	−	0.906585i	$-0.361320\pi$
$911$	1.75468e13	0.844045	0.422022	+	0.906585i	$0.361320\pi$
$912$	−4.37970e13	−2.09637
$913$	−7.12261e12	−0.339251
$914$	−5.57217e12	−0.264099
$915$	−8.64827e13	−4.07882
$916$	1.50175e12	0.0704801
$917$	−3.49366e12	−0.163162
$918$	0	0
$919$	5.57783e12	0.257956	0.128978	−	0.991647i	$-0.458830\pi$
$919$	5.57783e12	0.257956	0.128978	+	0.991647i	$0.458830\pi$
$920$	−1.52125e13	−0.700092
$921$	−2.79675e13	−1.28081
$922$	−7.08106e12	−0.322708
$923$	3.45402e12	0.156645
$924$	−5.30057e13	−2.39221
$925$	−1.06532e13	−0.478458
$926$	−1.21214e13	−0.541755
$927$	5.12476e13	2.27937
$928$	2.13438e13	0.944728
$929$	−2.46767e13	−1.08697	−0.543483	−	0.839420i	$-0.682895\pi$
$929$	−2.46767e13	−1.08697	−0.543483	+	0.839420i	$0.682895\pi$
$930$	−5.72316e12	−0.250878
$931$	−3.42618e13	−1.49464
$932$	1.68911e13	0.733308
$933$	−2.61116e13	−1.12815
$934$	4.71779e11	0.0202851
$935$	0	0
$936$	4.15966e12	0.177140
$937$	3.72310e13	1.57789	0.788944	−	0.614465i	$-0.210628\pi$
$937$	3.72310e13	1.57789	0.788944	+	0.614465i	$0.210628\pi$
$938$	3.33885e12	0.140827
$939$	5.93716e13	2.49220
$940$	−2.08767e13	−0.872140
$941$	2.09390e13	0.870569	0.435284	−	0.900293i	$-0.356648\pi$
$941$	2.09390e13	0.870569	0.435284	+	0.900293i	$0.356648\pi$
$942$	9.52803e12	0.394252
$943$	−1.14491e13	−0.471485
$944$	−2.95692e13	−1.21190
$945$	7.95645e13	3.24546
$946$	−8.90468e12	−0.361500
$947$	−3.50065e13	−1.41440	−0.707202	−	0.707011i	$-0.750043\pi$
$947$	−3.50065e13	−1.41440	−0.707202	+	0.707011i	$0.750043\pi$
$948$	−3.51255e13	−1.41249
$949$	4.69485e12	0.187899
$950$	4.47916e12	0.178419
$951$	2.15950e13	0.856132
$952$	0	0
$953$	4.83362e12	0.189825	0.0949127	−	0.995486i	$-0.469743\pi$
$953$	4.83362e12	0.189825	0.0949127	+	0.995486i	$0.469743\pi$
$954$	−5.24646e11	−0.0205068
$955$	−4.31682e13	−1.67938
$956$	3.88329e13	1.50363
$957$	5.76927e13	2.22340
$958$	−1.47603e13	−0.566176
$959$	−1.54606e12	−0.0590260
$960$	2.54413e13	0.966761
$961$	−2.23520e13	−0.845399
$962$	1.57368e12	0.0592419
$963$	−2.08408e13	−0.780902
$964$	−1.39051e13	−0.518595
$965$	−1.35729e12	−0.0503849
$966$	2.09717e13	0.774885
$967$	2.43474e13	0.895436	0.447718	−	0.894175i	$-0.352237\pi$
$967$	2.43474e13	0.895436	0.447718	+	0.894175i	$0.352237\pi$
$968$	2.68819e12	0.0984057
$969$	0	0
$970$	8.22971e12	0.298478
$971$	−1.35465e13	−0.489034	−0.244517	−	0.969645i	$-0.578629\pi$
$971$	−1.35465e13	−0.489034	−0.244517	+	0.969645i	$0.578629\pi$
$972$	−1.33322e13	−0.479076
$973$	−9.55057e12	−0.341603
$974$	−7.49614e12	−0.266884
$975$	2.46422e12	0.0873289
$976$	4.04933e13	1.42843
$977$	3.05916e13	1.07418	0.537090	−	0.843525i	$-0.319524\pi$
$977$	3.05916e13	1.07418	0.537090	+	0.843525i	$0.319524\pi$
$978$	1.53679e12	0.0537142
$979$	−5.71090e13	−1.98693
$980$	2.76501e13	0.957589
$981$	−3.68091e13	−1.26895
$982$	−2.54931e11	−0.00874825
$983$	−8.75389e12	−0.299027	−0.149514	−	0.988760i	$-0.547771\pi$
$983$	−8.75389e12	−0.299027	−0.149514	+	0.988760i	$0.547771\pi$
$984$	−1.41923e13	−0.482585
$985$	3.67492e13	1.24390
$986$	0	0
$987$	6.06157e13	2.03310
$988$	6.23312e12	0.208113
$989$	−3.31897e13	−1.10311
$990$	−2.51557e13	−0.832297
$991$	9.06157e12	0.298450	0.149225	−	0.988803i	$-0.452322\pi$
$991$	9.06157e12	0.298450	0.149225	+	0.988803i	$0.452322\pi$
$992$	9.75332e12	0.319779
$993$	−5.76068e13	−1.88019
$994$	1.47113e13	0.477983
$995$	1.19743e13	0.387299
$996$	−1.56249e13	−0.503095
$997$	−1.22306e13	−0.392030	−0.196015	−	0.980601i	$-0.562800\pi$
$997$	−1.22306e13	−0.392030	−0.196015	+	0.980601i	$0.562800\pi$
$998$	−1.06381e13	−0.339451
$999$	−8.66290e13	−2.75181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.17	yes	36
17.16	even	2		289.10.a.g.1.17	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.17	✓	36	17.16	even	2
289.10.a.h.1.17	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-7.00956 q^{2} +248.596 q^{3} -462.866 q^{4} -1624.49 q^{5} -1742.55 q^{6} -8782.15 q^{7} +6833.38 q^{8} +42117.0 q^{9} +O(q^{10})\)	\(q-7.00956 q^{2} +248.596 q^{3} -462.866 q^{4} -1624.49 q^{5} -1742.55 q^{6} -8782.15 q^{7} +6833.38 q^{8} +42117.0 q^{9} +11386.9 q^{10} -52453.2 q^{11} -115067. q^{12} +14453.2 q^{13} +61559.0 q^{14} -403841. q^{15} +189088. q^{16} -295222. q^{18} -931720. q^{19} +751920. q^{20} -2.18321e6 q^{21} +367674. q^{22} +1.37040e6 q^{23} +1.69875e6 q^{24} +685836. q^{25} -101311. q^{26} +5.57701e6 q^{27} +4.06496e6 q^{28} -4.42440e6 q^{29} +2.83075e6 q^{30} -2.02178e6 q^{31} -4.82412e6 q^{32} -1.30397e7 q^{33} +1.42665e7 q^{35} -1.94945e7 q^{36} -1.55332e7 q^{37} +6.53095e6 q^{38} +3.59301e6 q^{39} -1.11007e7 q^{40} -8.35453e6 q^{41} +1.53033e7 q^{42} -2.42190e7 q^{43} +2.42788e7 q^{44} -6.84186e7 q^{45} -9.60592e6 q^{46} -2.77645e7 q^{47} +4.70066e7 q^{48} +3.67726e7 q^{49} -4.80741e6 q^{50} -6.68990e6 q^{52} +1.77712e6 q^{53} -3.90924e7 q^{54} +8.52096e7 q^{55} -6.00118e7 q^{56} -2.31622e8 q^{57} +3.10131e7 q^{58} -1.56378e8 q^{59} +1.86924e8 q^{60} +2.14150e8 q^{61} +1.41718e7 q^{62} -3.69878e8 q^{63} -6.29983e7 q^{64} -2.34791e7 q^{65} +9.14023e7 q^{66} +5.42382e7 q^{67} +3.40677e8 q^{69} -1.00002e8 q^{70} +2.38979e8 q^{71} +2.87802e8 q^{72} +3.24831e8 q^{73} +1.08881e8 q^{74} +1.70496e8 q^{75} +4.31262e8 q^{76} +4.60652e8 q^{77} -2.51854e7 q^{78} +3.05262e8 q^{79} -3.07172e8 q^{80} +5.57434e8 q^{81} +5.85616e7 q^{82} +1.35790e8 q^{83} +1.01053e9 q^{84} +1.69764e8 q^{86} -1.09989e9 q^{87} -3.58433e8 q^{88} +1.08876e9 q^{89} +4.79584e8 q^{90} -1.26930e8 q^{91} -6.34313e8 q^{92} -5.02607e8 q^{93} +1.94617e8 q^{94} +1.51357e9 q^{95} -1.19926e9 q^{96} +7.22732e8 q^{97} -2.57760e8 q^{98} -2.20917e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more